The line L given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line K is parallel to line L and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between L and K is _________ units.

The equation of the line passing through the point of intersection of the lines $3 x-y=5$ and $x+3 y=1$ and making equal intercepts on the axes is

The equation of pair of lines $y=p x$ and $y=q x$ can be written as $(y-p x)(y-q x)=0$. Then the equation of the pair of the angle bisectors of the lines $x^2-4 x y-5 y^2=0$ is

The number of possible distinct straight lines passing through $(2,3)$ and forming a triangle with co-ordinate axes whose area is 12 sq . units are,